Question

The \( Z \) parameter \( Z_{21} \) of the following circuit is

• A. \( Z_2 \)
• B. \( Z_1 \)
• C. \( Z_1 + Z_2 \)
• D. \( -Z_2 \)

Hint:

For \( Z_{21} \), trace the path from input current at port 1 to voltage at port 2 while keeping \( I_2 = 0 \).

Answer 1

The Correct Option is A

The Z-parameters relate the port voltages and currents of a two-port network using the following equations:

\[ \begin{aligned} V_1 &= Z_{11} I_1 + Z_{12} I_2 \\ V_2 &= Z_{21} I_1 + Z_{22} I_2 \end{aligned} \]

We are asked to find \( Z_{21} \), which is defined as:

\[ Z_{21} = \left. \frac{V_2}{I_1} \right|_{I_2 = 0} \]

Step-by-step approach:

• To find \( Z_{21} \), we set \( I_2 = 0 \), which means the output port is open-circuited (no current flows out of port 2).
• Inject a current \( I_1 \) at port 1.
• Since the output is open-circuited, the entire current \( I_1 \) flows only through the path containing \( Z_2 \).

Observation: Under open-circuit condition at port 2, \( Z_1 \) does not contribute to \( V_2 \) because no current flows through it. Therefore, the voltage \( V_2 \) appears directly across \( Z_2 \).

\[ V_2 = I_1 \cdot Z_2 \Rightarrow Z_{21} = \frac{V_2}{I_1} = Z_2 \]

Final Answer: \( \boxed{Z_{21} = Z_2} \)